I had this same problem as well and the way I fixed it was first unscrewing it taking off the upper part and putting a thin piece of tape on the right clicker block, i wouldn't recommend putting tape on the actual clicking mechanism though as it will probably just get sticky and be more difficult to click, sorry if the explaination is vague but this solved my problem

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Because you don't list what model Logitech cordless mouse you have, look in this list to see if yours is on it. If it is, click on the link and download and install the driver. This
download has the latest drivers and SetPoint software for Logitech
cordless, wireless and Bluetooth pointing devices (mouse). http://www.softwarepatch.com/utilities/logisetpoint-dl.htmlSpecifically
the mouse driver is for the following models:

Anywhere Mouse MX

Cordless Mini Optical Mouse

Cordless Optical Mouse

Cordless Optical TrackMan

Cordless TrackMan Optical

Cordless TrackMan Wheel

G1 Optical Mouse

G3 Laser Mouse

G5 Laser Mouse

G500 Gaming Mouse

G7 Laser Cordless Mouse

G9 Laser Mouse

G9x Laser Mouse

LS1

LX3

LX3 Plus Laser

LX5

LX6

LX7

LX8

M110

M205

M305

M500

M505

M555b

M705

MX 610

MX 610 Left-Hand

MX 620

MX Revolution

MX1100

Optical Mouse

Performance Mouse MX

Racer Mouse

Spot Mouse

Tiger Mouse

Trackman Marble

TrackMan Wheel

Trackman Wheel

V100

V150

V200

V220

V320

V400

V450

V470

V500

V550

VX Nano

VX Revolution

Zebra Mouse

I hope this helps and good luck! Please remember to vote and leave a testimonial.

I love this trackball mouse, yet they are very sensitive to wear and trash that causes them to fail. Wal-Mart sells great ones like the Logitech LX3 optical mouse that are not as sensitive and have more features